Question: Simplify the following expression: $ p = \dfrac{1}{9} - \dfrac{-8q + 5}{8q} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8q}{8q}$ $ \dfrac{1}{9} \times \dfrac{8q}{8q} = \dfrac{8q}{72q} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-8q + 5}{8q} \times \dfrac{9}{9} = \dfrac{-72q + 45}{72q} $ Therefore $ p = \dfrac{8q}{72q} - \dfrac{-72q + 45}{72q} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{8q - (-72q + 45) }{72q} $ Distribute the negative sign: $p = \dfrac{8q + 72q - 45}{72q}$ $p = \dfrac{80q - 45}{72q}$